14.02 - Spring 2014

Macroeconomics and the Financial Crisis

Francesco Giavazzi

February 2014

1

Outline of the Course

Part 1: Origins of the 2007-13 economic crisis: why did a failure of the�nancial system (of banks in particular) produce the largest recessionsince the Great Depression of the 1930s?

I The �nancial system (banks) is the core of the economy. We cannotunderstand macroecononmics if we do not understand how shocksand policies a¤ect the economy through their e¤ects on the�nancial system, banks in particular

I Why do banks exist? Why are they fragile institutions?I Four small models

I Leverage, Moral Hazard, Maturity MismatchI Borrowing constraints & ampli�cation of economic shocks

2

Outline of the Course

Part 2: The policy response to the �nancial crisis

I Background models (�traditional�macroeconomics)

I The Fed�s response: interest rates and "quantitative easing"

I Fiscal policy: President Obama�s "Stimulus Program"

I Did these policies work?

I Legacy of the crisis: Debt and the Eurocrisis

3

Macroeconomics and the Financial System

I Understanding banks

I balance sheets

I leverage

I non-linearities

4

Balance Sheets

I The balance sheets of banks and other �nancial �rms are centralto understanding how a �nancial system works and why in 2007-08it blew up

I Before studying the �nancial system we thus need to understandwhat a balance sheet is. We do it in 3 steps:

I de�nitionI balance sheet of a householdI balance sheet of a bank

5

Balance sheets explained to your younger brother

Assets Liabilities

Saving for a rainy day Other people�s moneyMoney working for you Own skin in the game

I Assume you wished to set up a company and to start you need 100K$. You have 10K of your own (yourskin in the game) and borrow 90K from a bank. You then spend 95k to start the company (this is the

money working for you) and leave 5K in the bank as a bu¤er in case something (small) goes wrong

I You can loose Your skin in the game. If you loose more, i.e. Other people�s money, you are bankrupt. Your

skin in the game is the bu¤er against possible losses: the smaller the bu¤er, the smaller the losses you can

withstand without going bankrupt.

I Accountants call

I Other people�s money: Debt

I Your Skin in the Game: Equity

I Saving for a rainy day: Reserves

I Leverage Assets= Your Skin in the Game =AssetsEquity6

Example: the balance sheet of a household

I Consider a household which bought a house �nanced by a mortgage

I How large is the mortgage as a fraction of the value of the houseobviously makes a big di¤erence

I Also the type of mortgage makes a di¤erence: is the interest rate�xed, or does it �oat with market rates? At current interest ratesand at current house prices the household may look perfectly able tomake the mortgage payments, but what if house prices fall, orinterest rates rise?

I To understand how risky is the position of this household we needto know its balance sheet, i.e. the value of the house and the sizeand conditions of the mortgage.

7

Balance sheet of a household (thousand US $)

Assets Liabilities

House 1.000 Mortgage 900Stocks 50 Equity 160

Bank deposits 10

I this family has purchased a house with a downpayment of 100 and amortgage worth 900. Its net worth (its Equity) is 160: 100 (equityin the house) + 60 (cash and stocks)

I its leverage (the ratio of Assets to the family�s net worth) is1060/160 = 6.625

8

Balance sheet of a household (thousand US $)

I Assume house prices fall 30% and the value of the house falls to700. The family is broke: it�s net worth has become negative:60+ (100 300) = 140 (because the 100 of equity in thehouse is less than the fall in the value of the house)

Assets LiabilitiesHouse 700 Mortgage 900Stocks 50 Net worth 140

Bank deposits 10

I If the interest rate on the mortgage remains unchanged, he family isstill able to make its monthly mortgage payment: just looking at�ows (monthly income and monthly mortgage payments) we wouldnot have guessed the family could be in trouble.

I The problem is that this family had too much debt. What wouldhave happened if its leverage had been 2 instead of 6.625?

I But what does "being broke" mean in practice?9

� �

�

Balance sheet of a household: the youwalkaway.comsolution

I Assume the mortgage is a non-recourse loan, i.e. if the borrower isdelinquent the bank has only the right to re-possess the house. Nowthe bank is broke (its equity,140 is not su¢ cient to absorb the loss,200)

household bankAssets Liabilities Assets Liabilities

House 1000 Mortgage 900 Mortgage 900 Deposits 760Stocks 50 Net worth 160 Equity 140

Bank deposits 10

household bankAssets Liabilities Assets Liabilities

House 0 Mortgage 0 House 700 Deposits 760Stocks 50 Net worth 60 Equity 60

Bank deposits 1010

�

Balance sheet of a household: when the bank can seize allyour assets

I Assume instead that the mortgage contract gives the bank the rightto reclaim not only the house, but any other households�assets.Now the bank survives: its equity is zero but not negative.

household bankAssets Liabilities Assets Liabilities

House 1000 Mortgage 900 Mortgage 900 Deposits 760Stocks 50 Net worth 160 Equity 140

Bank deposits 10

household bankAssets Liabilities Assets Liabilities

House 0 Mortgage 0 House 700 Deposits 760Stocks 0 Net worth 0 Assets 60 Equity 0

Bank deposits 011

The Balance Sheet of a Bank

I Remember what is Leverage

I Leverage Assets= Assets=Your Skin in the Game Equity

12

Leverage and Fragility

I The balance sheet of banks is crucial to understandI their role in transferring savings from households to �rmsI why they are fragile institutions

I remember that the reason banks hold equity is to absorbpossible losses on the assets they own

I how much equity should a bank have is the central question inthe current debate about reforming the �nancial system andthus avoid another �nancial disaster

I Thus there is a tradeo¤I the more equity a bank holds, the larger its bu¤er, the strongerthe bank is, i.e. the less likely it goes bankrupt

I the more equity a bank has, the lower its pro�tability: thisexplains why raising equity is di¢ cult

13

Leverage

I Assume a bank has an amount of debt (e.g. deposits) D andan amount of equity (K̄ ) also called capital. Its liabilities areL = D + K̄ , equal to its total assets

I The bank holds two types of assets

I loans and other investments (what we called Money workingfor you)

I reserves (what we called Savings for a rainy day)

I Let α be the fraction of total assets invested, and (1 α) thefraction kept as reserves

I Investment is risky: for each dollar invested today you get pdollars tomorrow; where p is a random variable. We mayassume E (p) 1 still with some probability p 1

14

�

LeverageThe Bank�s Balance Sheet today

Assets Liabilities(1 α) L (reserves) L = D + K̄ (equity)

αL (loans and other risky investments)

The Bank�s Expected Balance Sheet tomorrow

Assets Liabilities(1 α) L Deposits: Dp (αL) Capital: K̄ + (p 1) (αL)

I Here we see why banks hold equity: in order to be able toabsorb losses (or gains) on their assets. Note that the capitaltomorrow is equal to the original capital plus the realizedcapital gain (p 1) (αL)� which is a capital loss for p 1

I The bank�s leverage ratio is Assetsλ = Capital =L

Capital , the ratio oftotal assets (equal to total liabilities) to capital15

�

��

�

16

Leverage

If K̄ + (p � 1) (αL) < 0 the bank is broke.Note that we can rewrite the condition as

K̄ + (p � 1) (αL) < 0

K̄ + p (αL)� (αL) < 0

K̄ + p (αL)� (αL) + (1� α) L < (1� α) L

K̄ + p (αL) + (1� α) L < L

p (αL) + (1� α) L < L� K̄p (αL) + (1� α) L < D

The last line says that the bank is broke when the value of assets isnot enough to pay for deposits

The possibility that the bank defaults (becomes unable to pay itsdebt) introduces a non-linearity

Leverage and the probability that the bank defaults

What is the probability that a bank will go broke?

K̄Prob (K̄ (1 p) (αL) 0) = Prob

�p 1

αL

�which is increasing in α : for a given value K̄ , the higher thefraction of total assets the bank invests in the risky asset, thehigher the probability it goes broke.How do banks choose α? They choose it so that the probability ofgoing broke is less than or equal to some number� say 5%

KPr

� ¯ob p 1 0

αL

�� .05

For given K̄ the above inequality determines the value of α.

17

� � �

�

Leverage and Value at Risk (VAR)

j (1 p) αL j is also called the bank�s Value at Risk. K̄ should belarge enough to absorb a loss equal to j (1 p) αL j which occurswith a 5% probability

18

��

Leverage and VARThe bank has two choices to make: α and K̄ . Using the expressionfor the leverage ratio ( Lλ = ¯ ), the probability that a bank will goKbroke is

Prob�

K̄p 1

αL

�= Prob

�p 1

1αλ

�I for given α, the probability that a bank will go broke is anincreasing function of the leverage ratio λ. To reduce λ thebank canI keep its assets, L, constant but �nance them with less debtand more equity (remember, L = K̄ +D)

I keep K̄ constant but reduce L � for example reducing loans to�rms and households� thus reducing D

I for given 1α, the value of λ such that Prob p 1 αλ

�� 5%

is decreasing with Var (p) 1

1This is strictly true if the ditribution of p is Normal. It is not true for someother distributions.

19

� �

��

Leverage of U.S. and European banks before the crisisU.S. banksCitigorup 19.2

JPMorgan 12.7

Wells Fargo 12.0

Bank of America 11.7

European banksUBS 53.4

Credit Suisse 22.7

Fortis 25.5

Dexia 36.8

BNP Paribas 28.5

Barclays 37.8

Royal Bank of Scotland 21.7

Deutsche Bank 52.0

Banks may have a high λ and still be safe by keeping α low�and indeedthis was thought to be the case for European banks which own lots of"safe" government bonds. This is why Deutsche Bank was consideredsafe even with a value of λ almost three times that of Citi.

20

Leverage and the Crisis

I In the years before the crisis macroeconomic volatility was low, thusVar (p) was low

I low Var (p) meant that banks, for given α, could a¤ord a relativelyhigh λ� or, for given λ, they could a¤ord a higher α (they couldhold a higher share of risky assets)

I at the start of the crisis volatility suddenly increased and banksresponded by lowering both λ and α

I but this takes time because raising capital and reshu­ ing the bank�sassets takes time

I reducing α is also dangerous because

I if the bank reduces its lending to �rms (or stops lending to�rms), investment will fall

I if it sells other risky assets, such as shares, it pushes shareprices down precisely at a time when the stock market(beacuse of the crisis) is already falling. This could generate anegative leverage cycle

21

Leverage Cycles and Fire SalesAssume for simplicity α = 1. The bank�s iinitial balance sheet (withleverage = 10) is

Assets Liabilities110 Deposits 99

Capital 11

Balance sheet after the fall in asset prices (leverage = 10,9)

Assets Liabilities109 Deposits 99

Capital 10

The bank can return to a leverage ratio of 10 selling assets and payingback deposits

Assets Liabilities100 Deposits 90

Capital 10

The bank ignites a �re sale: it sells assets precisely when asset prices arefalling !22

Raising Capital to Avoid Fire Sales

Balance sheet after the fall in asset prices (leverage = 10,9)

Assets Liabilities109 Deposits 99

Capital 10

The bank can return to a leverage ratio of 10 instead of selling assets, byrasing capital

Assets Liabilities110 Deposits 99

Capital 11

23

How does this help us understand what happened since2008?Phase I: Bank Losses (writedowns) and Re-capitalizations: 08/2007 - 08/2008

© Bloomberg. All rights reserved. This content is excluded from our Creative Commonslicense. For more information, see http://ocw.mit.edu/help/faq-fair-use/.

24

© IMF. All rights reserved. This content is excluded from our Creative Commons

license. For more information, see http://ocw.mit.edu/help/faq-fair-use/.

Source: Figure. 1.3 in International Monetary Fund. "World Economic Outlook:Sustaining the Recovery." October 2009.

25

The Leverage of European Banks and the Crisis in theEuro Area

European banks:UBS 53.4Credit Suisse 22.7Fortis 25.5Dexia 36.8BNP Paribas 28.5Barclays 37.8Royal Bank of Scotland 21.7Deutsche Bank 52.0

I High leverage was not a problem so long as α was low becausegovernment bonds were considered safe. But when this assumptionno longer held, European banks found they had far too little capital

I This in turn made government debt more risk because theassumption was that governments would bail out the banks if theywent bankrupt26

The Financial System

I What is the �nancial system? What role does it play in theeconomy?

I The role of the �nancial system is to transfer the savings ofhouseholds to those who need the funds to �nance realeconomic activity, e.g. set up a new company or expand anexisting one

I How can this be done? Start from the simplest case: the economyof Robinson Crusoe

27

Robinson Crusoe�s Economy

I Robinson has a project: a land to farm. In his economy there is no�nancial system, because Robinson has no one with whom to trade

Assets Liabilities

Projects Equity

Projects (farming) are wholly owned by the farmer (Robinson). Inthis economy there is no borrowing, and no "delegation", thus noneed to monitor the managers who carry out the projects.

28

Financial System and DelegationI Who owns the capital rarely is the best person to run a projectwhich uses that capital

I Modern economies work thanks to contracts that allow to delegatethe running of projects to more skilful individuals

I The �nancial system provides the institutional framework for thosecontracts

Delegation to a project manager without �nancialintermediaries

Firm�s balance sheet Household�s balance sheet

Assets Liabilities Assets Liabilities

Projects Debt Firm�s bondsEquity Firm�s shares Equity

29

Financial System and Delegation via Banks

Bank�s balance sheet

Assets LiabilitiesLoans to �rms Deposits

Other assets Equity (shares issued by the bank)

Firm�s balance sheet Household�s balance sheet

Assets Liabilities Assets Liabilities

Projects Debt (Bonds) Firm�s bondsBank loan Shares of �rms and banksShares Bank deposits Equity

30

Why do banks exist?

I Banks (and other �nancial �rms) exist because people in theeconomy are di¤erent: they have di¤erent skills and di¤erentneeds� in economists�jargon they are heterogeneous

I Banks (and the �nancial system more generally) help solving theproblems posed by this heterogeneity

31

Two examples of heterogeneity - 1: Heterogeneity wrt skills

I Entrepreneurs are very special individuals. Their characteristic is tohave the skills necessary to turn ideas into projects and then runthem. They do this borrowing from people who do not have theseskills. Investors (those who own the capital) are happy to lend toentrepreneurs because they hope to participate in the returnsproduces by the e¢ cient exploitation of smart ideas

I The contract between a lender and an entrepreneur is complicated

I entrepreneurs may not have the incentive to run their projectdiligently enough. Once they have raised the funds frominvestors they may prefer to spend time on the beach

I lenders (investors) cannot observe how diligently theentrepreneur is running her project, thus they can be fooled

I this "lack of trust" can be overcome if entrepreneurs risk enough oftheir own in the project

I banks can facilitate the contract between entrepreneurs and lenders,monitoring the entrepreneurs

32

Two examples of heterogeneity - 2: Heterogeneity wrtliquidity needs

I Agents have di¤erent preferencesI some wish to hold very liquid assets (demand deposits)I other need to borrow long term, e.g. a 30-year mortgage tobuy a house or to build a new plant.

I Another role banks can play is associated with the fact that theycan transform maturities, i.e. borrow by issuing demand depositsand lend for 30 years

I We shall now study two models which describe some themechanisms underlying these two reasons why banks exist. In both,as we shall see, balance sheets are central. (Of course our list ofreasons why banks exist is not exhaustive: there are a few more, likethe fact that banks may be better at evaluating the �rms�projects.)

1. Entrepreneurs, banks and small investors2. The bene�ts and the risks of transforming maturities and providingliquidity33

1. Why do banks exist? Entrepreneurs, banks and smallinvestors

[Bengt Holmostrom and Jean Tirole, "Financial intermediation, loanablefunds and the real sector", Quarterly Journal of Economics, 1997]

There are 3 actors in the economy: entrepreneurs, small investorsand banks

Entrepreneurs

I there are many of them; each one hasI an idea that costs I dollars to implementI an amount A of cash they can dedicate to their idea, A I

I an idea implemented today will produce tomorrowI R 0 with prob pI 0 with prob (1 p)

I if they don�t invest their cash in their idea, entrepreneurs canbuy a safe government bond whose total return is 0 γI R

34

�

The contract between entrepreneurs and small investors

Since A I , the idea, to be implemented, needs outside funding.Assume there are only small investors. They are small in the sensethat they do not have the resources to monitor how diligently theentrepreneur whom they have �nanced runs her project

I Entrepreneurs can a¤ect p, the probability of success, bydeciding how much e¤ort to put into running their project.This creates a moral hazard if their e¤ort cannot be observed

I If they put little e¤ort they enjoy a private bene�t B (e.g.they spend more time on the beach, less on their project)I if private bene�ts are 0, p = pHI if private bene�ts are B, p = pL pH

I Small investors do not observe the entrepreneur�s e¤ort. Theiroutside option (if they do not invest in the project) is buyingthe safe government bond.

35

The contract between entrepreneurs and small investors

We assume that returns are such that investing in theentrepreneur�s idea yields a higher return than investing in a safegovernment bond only if the entrepreneur puts in enoughe¤ort:

I pHR γI

I pLR + B γI

36

How to make sure that entrepreneurs are diligent

To make sure that she works hard and thus achieves pH , smallinvestors need to o¤er the entrepreneur a contract that issu¢ ciently attractive to induce her to work hard. Consider thefollowing contract:

I if the project succeeds R will be divided between RE for theentrepreneur and RS for the investors with RE such that theentrepreneur has an incentive to put in pH

I RE must satisfypHRE � pLRE + B

i.e.RE � B/ (pH pL) = B/∆p

I Note that, as pL ! pH , the contract becomes unfeasiblebecause giving the entrepreneur the necessary incentivebecomes impossible

37

�

Pledgeable income

I Since RE � B/∆p for the entrepreneur to be credible whenhe commits not to shirk, not all the income produced by theproject can be pledged to outside (small) investors

RS � (R B/∆p) R

I Limited pledgeability arises because of the moral hazardproblem of entrepreneurs

I Limited pledgeability is what makes contract theory (a livelybranch of economics) interesting. It is also what opens up anintrusting role for �nancial intermediaries (banks) becausesometimes they can attenuate the moral hazard problem

38

�

39

To have an incentive to be diligent the entrepreneur mustcontribute a minimum of her own to the project

I Consider the small investor. If he does not �nance the project,his alternative is to buy the safe bond with a return γ. Thushe will only invest if

pHRS � γ (I � A)I and since

RS � (R � B/∆p)I small investors will lend as long as

_A = A(γ) � I � [pH/γ (R � B/∆p)]

i.e. unless the entrepreneur contributes a minimum amount of_her own, A(γ), she cannot credibly commit to pH

I which will be the return for small investors when they invest inthe project? Competition among them will bring it down to γ,the return on their alternative option, which is investing insafe bonds

How can banks helpBanks can �nance the entrepreneur�s project. But di¤erently fromsmall investors they can also monitor how diligently she runs it.They cannot control the entrepreneur perfectly (i.e. make sureB = 0) but, by spending some money, they can avoid "extreme"negligence, i .e. they can reduce the entrepreneur�s outside bene�tto b B . When the entrepreneur enjoys b the prob of successremains pL. The bank�s monitoring cost is c 0.

I if the project succeeds, R will be shared: R = RE+ RS + RBI the entrepreneur must be guaranteed

RE � b/∆p

where the only di¤erence is that now b BI the bank must be guaranteed a total gross return RB largeenough to make sure it has the incentive to monitor

pHRB c � pLRBi.e.

RB � c/∆p40

�

The minimum amount the bank must contribute to becredible when it says it will monitor the entrepreneur

I Let IB be the amount the bank contributes to the project. Howlarge should IB be?

I To determine this value we need to start from the bank�s outsideoption: call β the return the bank can obtain if it invests elsewherein the economy. The bank must therefore be guaranteed a total netreturn (that is net of the monitoring cost) at least equal to βIB ,where

βIB = pHRB c = c(pH/∆p 1)

using RB � c/∆pcp

IB =L

β∆p

I For any given value of the bank�s outside option, β, this value of IBis the minimum amount the bank must contribute to be crediblewhen it says it will monitor the entrepreneur

41

� �

The amount the bank will be asked to contribute

I Because monitoring is costly, the entrepreneur will �nance throughthe bank as little of the project as possible, that is no more thanI cpB = L . The reason is that in order to o¤er the bank a net return∆pequal to β, the entrepreneur must pay a gross return larger than β,that is large enough to cover monitoring costs

I assume for instance, that the bank�s outside option� its returnif it invests elsewhere in the economy� is γ, equal to theoutside option of small investors. Then the gross return theentrepreneur must pay the bank per unit it invests in theproject is γ+ c/IB γ. Even in this case the entrepreneurwill not fund more than IB from the bank

I Finally note that a bank that has no capital� and thus cancontribute nothing of its own to the project� and simply �nances allits loans to �rms issuing deposits is useless � at least if we thinkthat the main reason why banks exist is to monitor �rms

42

What is there for small investors?

I When RE and RB are such that the entrepreneur has anincentive to be diligent, and the bank has an incentive tomonitor, small investors get

RS = [R (b+ c) /∆p]

and must contribute I A IB . Since their alternativeremains the safe bond, they will �nance the project provided

γ [I A IB (β)] � pH [R (b+ c) /∆p]

I This condition can be re-written as

A � A(γ, β) = I IB (β) (pH/γ) [R (b+ c) /∆p]

43

�

� �

� � �

� � ��

Which Project Are Financed ? (returns are net returns)

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44

What can go wrong? (1)

A could fall (e.g. asset price shock from a bubble bursting)

Assume the entrepreneur contributes the real estate, for instancethe land where the project is developed. If real estate prices fall, A_will fall. If it falls below A(γ), projects that previously could be�nanced only by small investors, now need a bank because thevalue of what the entrepreneur contributes is no longer su¢ cient toattract small investors.

45

What can go wrong? (2)

c is too small (e.g. subprimes)

Remember that IB � c pH .p If the bank claims the cost ofβ∆monitoring, c , is small (or underestimates the cost of monitoring)it will contribute too little to the project. Ex-post it will have noincentive to do the monitoring. In this case the entrepreneur�sprivate bene�t will remain B because

bRE = ∆p

B∆p

and p = pL

46

What can go wrong ? (3)

The bank may not have enough capital to credibly commit tomonitor entrepreneurs. Remember that the minimum amount abank must contribute to the project is I c p

B (β) = H tβ p . If i commits∆less then IB (β) its return is insu¢ cient to cover the cost ofmonitoring, thus the bank will not monitor.

47

What happened before and during the crisis ?

Each one of the three things that could go wrong has gone wrong:

1. c : before the crisis banks had reduced their direct investments inthe projects they had �nanced. They had done this selling theirloans to other investors (what is called securitization, assembling alarge number of mortgages and building a �nancial security whichcontains them all.) The bene�t was less exposure to risk; the costwas reduced incentive to monitor.

2. IB (β): banks�capital fell during the crisis. This means that bankshad less capital for direct lending.

3. A: the fall in real estate prices and in asset prices in general,reduced the value of A, the resources entrepreneurs could committo their projects.

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2. Why do banks exist? Second example: heterogeneitywrt preferences

I The second role banks play is associated with the fact that they can"transform maturities", i.e. borrow short (by issuing checkingaccounts) and lend long (e.g. for 30 years).

I This is useful because some agents in the economy wish to holdvery liquid assets (checking accounts), while other agents need toborrow long term, e.g. a 30-year mortgage to buy a house or tobuild a new plant, In other words people di¤er in their preferencesas to when they want to consume.

I Without a bank it would be hard to �nd a mortgage. Assume allhouseholds wished to keep their savings in checking accounts: thenwho would buy a 30-year mortgage?

49

A model of maturity transformation

[Diamond, D., and P. Dybvig "Bank runs, deposit insurance andliquidity", Journal of Political Economy, 1983]

There are 3 periods

I t = 0 agents start with 1 unit of endowment each. Investmentdecisions are made. 2 technologies are available:

I one delivers 1 unit of output in t = 1 for each unit of outputinvested in t = 0

I the other delivers R 1 units of output in t = 2 for each unitof output invested in t = 0. However, if this technology isliquidated in t = 1 it delivers L 1 units of output

I t = 1 and t = 2: agents consume

50

Agents�types

I There are 2 types of agents, and many agents of each type. Thesize of the population is normalized to 1.

I "patient", who consume only in t = 2 and nothing in t = 1I "impatient" who consume all in t = 1I agents learn their type only in t = 1 all they know in t = 0 isprob(being patient) = πprob(being impatient) = 1 π

I of course if you knew your type in t = 0 you could investeverything in one technology or the other.

51

�

The world of Robinson Crusoe: no banks and no one withwhom to trade

Call I the amount agents invest in the technology with return R att = 0. Then their consumption options are

I if impatient: cA1 = (1 I ) + LI = 1 (1 L) I � 1 (= 1 onlyfor I = 0)

I if patient: cA2 = (1 I ) + RI = 1+ I (R 1) � R (= R onlyfor I = 1)

where A stands for "Autarky", Robinson�s world

52

� � �

� �

Market economyIn t = 1 agents can trade.

I An agent who �nds out he is impatient can issue a bond thatpromises to pay 1 unit of good in t = 2, sell it and eat in t = 1.The price of this bond is p. p is a relative price that transformst = 2 goods in t = 1 goods

[units of t = 1 goods ]p =

[units of t = 2 goods ]

I Since the impatient agent will receive RI in t = 2, he can trade itfor p(RI ) units of t = 1 goods

I Similarly an agent who �nds out he is patient will trade (1 I )units of t = 1 goods,which he does not need, for (1 I )/p unitsof t = 2 goods

I ThusI cM1 = (1 I ) + pRI if impatient, where the superscipt Mrefers to the market equilibrium

I cM (1 )2

I= p + RI if patient53

��

�

�

Market economy (cont.)

I If 1/p R, agents choose I = 0 because by trading at price pthey can do better than investing at return R. Remember

[units of t = 2 goods ]1/p =

[units of t = 1 goods ]

ThuscM1 = 1, cM2 = 1/p.

I If 1/p R, agents choose I = 1 and

cM1 = pR, cM2 = R

54

Market economy (cont.)

Neither� p 1/R , nor p 1/R are feasible because they imply thatcM1 , c

M2 exceed the resources available to the economy

I p 1/R =) I = 1 cM = R and cM, 2 1 = pR 1: this isunfeasible

I p 1/R =) I = 0, cM1 = 1 and cM2 = 1/p R : this is also

unfeasible

55

Market economy (cont.)

The only feasible equilibrium is p = 1/R where agents choose

I cM1 = 1 if impatientI cM2 = R if patientI IM2 [0, 1]

The last task is �nding IM , the amount invested in the "long"technology. In order for these choices to be feasible IM must be such that

(1 π) cM1 = 1 IM

πcM2 = RIM

So IM must be equal to π.

56

� �

Why the market outcome is (in general) not optimalThe market equilibrium is:

I cM1 = 1 if impatientI cM2 = R if patient

i.e. agents who �nd out they are impatient forgo R and consume 1 R.

I the market economy yields the same allocation agents would havechosen had they known their type in t = 0.

I i.e. it eliminates the ine¢ ciency caused by uncertainty (the Autarkicequ� ilibrium is ine¢ cient: there is always some liquidation).

I cM M1 = 1, c2 = R

may not be the best solution. If in t = 0

agents could insure against the possibility that in t = 1 they �ndoun t they are impatient, they might wish to consumec M M1� c1 = 1, c

� c2 = R

owhere � denotes optimal2

consumption levels. How could they insure? 22We are assuming that agents give identical importance to

consumption in the two periods, i.e. there is no discounting. In otherwords agents maximize U = (1 I Pπ) u(c1) + πu(c2 ). They will wish toinsure provided (1 π) u0(1) πu0(R) where u0 is the marginal utility ofconsumption.

57

��

How can a bank improve upon the market outcome

I Assume we want to achieve fc1� 1, c2� R, c1

� c2�g

I in t = 0 the bank issues demand deposits: in exchange for adeposit of one unit at t = 0, agents receive either c1

� at t = 1, orc2� at t = 2. To achieve this the bank, in t = 0 stores (1 π) c1

�

and invests πc2�/R in the technology which yields R in t = 2 (of

course subject to the constraint (1 π) c1�+πc2

�/R = 1)I the bank achieves the optimal allocation provided no individualwithdraws at t = 1 unless she does not have to, i.e. unless shediscovers she is impatient. No patient consumer withdraws in t = 1

I provided c1� c2

� this assumption is not unreasonable because itwould be irrational for a "patient" consumer to withdraw at t = 1pretending he is impatient.

58

�

�

Bank runs: why can they happen

I suppose a patient consumer anticipates that all other patientconsumers will pretend they are impatient and withdraw c1

� at t = 1

I at t = 1 the bank must then liquidate all its long term investment.The total amount of resources available to the bank are(1 π) c1

� + π (c2�/R) L c1

� if c2�/c1

� R/L

I thus for 1 c2�/c1

� R/L, if depositors anticipate that a largeenough number of them will want to withdraw early, the bank fails

I note that 1 c2�/c1

� R/L always holds for c1� c2

� andc1� 1, c2

� RI bottom line: bank runs can happen because banks may be solventbut illiquid , i.e. their assets are not readily convertible into cash(here consumption).

59

�

Bank runs: when can they happen

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60

Bank runs: possible remedies

I Narrow banking. The bank invests nothing in the illiquid technologyand stores everything

I Suspension of convertibility. The bank has the option of stop payingits depositors when it runs out of cash. This means that any clientwho shows up "late" will see her/his deposit transformed from ademand deposit to a 2-period bond

I Deposit insurance. The government steps in when the bank runsout of cash

61

Inside and Outside Liquidity

We have already seen an example of liquidity crises in the model of"bank runs". Here we discuss a model that further highlights theimportance of liquidity

[ J. Tirole, Illiquidity and all its Friends, mimeo, 2010 andInside and Outside Liquidity, MIT Press, 2010]

I Two types of liquidityI inside liquidity: liquidity provided by markets participantswith no outside intervention

I outside liquidity: liquidity provided by the governmentthrough its ability to borrow against future tax revenues

I Two questionsI Is inside liquidity su¢ cient, or, in order to prevent liquidationof otherwise pro�table projects, outside liquidity is needed?

I Inside liquidity need not only be su¢ cient in the aggregate. Italso needs to be dispatched to those who need it62

Liquidity shocksI Three periods. The interest rate between each two subsequentperiods is zero� meaning that if you do not invest in thisproject your alternative is a net return equal to zero.

I t = 0I an entrepreneur �nances a project whose initial cost is 10,borrowing 2 from investors and contributing 8 in equity

I t = 1I with probability 1/2 there is an overrun (a "liquidity shock").An additional quantity, 20, of funds is needed to keep theproject running. Otherwise the project is liquidated and yieldsno income in t = 2

I with probability 1/2, there is no overrunI t = 2

I provided the overrun, if it happened, has been covered, andprovided the entrepreneur has put enough "e¤ort" in runninghis project, this produces a revenue of 30

I the revenue, 30, is then shared between the investors and theentrepreneur63

Pleadgeable income (what can be promised to investors)I in t = 0 the expected contribution of investors to the projectis 2+ (1/2)20 = 12. Assuming there are many investors whocompete with one another, 12 is all that must be promised tothem in t = 0 to bring them in (Remember that the interestrate is assumed to be zero)

I what goes to the entrepreneur, in case of a success, is 18.Assume that 18 is what is needed to make sure that theentrepreneur puts enough �e¤ort� into running the project(i.e. assume 18 is the amount that solves the incentiveproblem we studied in the Holmstrom-Tirole model)

I The income the entrepreneur can credibly pledge to outsideinvestors in t = 0 is thus P = 30 18 = 12 all that remainsgoes to the entrepreneur

I provided investors are promised 12 in case of success, they will�nance the project in t = 0 even if they know that (1) itmight need re�nancing and (2) in case of success, 18 will beturned over to the entrepreneur64

�

Finance as you goNow we are in t = 1

I if an overrun occurs, the entrepreneur will ask investors tocontribute 20

I but what looked feasible in t = 0 (remember that investorswere happy to be promised 12 knowing that they might beasked to cover an overrun) is no longer feasible in t = 1

I all the entrepreneur can promise is to deliver P = 12 in t = 2if the project succeeds. If he promised more investors wouldunderstand that he would not run it e¢ ciently

I but what is needed to keep the project going is 20 12.Looked at as of t = 1 no investor will cover the overrun andthe project will be abandoned

I trying to bring in "new" investors, o¤ering them seniority withrespect "old" investors doesn�t help. The project isabandoned even if the entrepreneur gave 0 to the old investorsand promised P to new ones

65

Insuring through a credit lineTo solve the problem that arises in t = 1 the entrepreneur can buyinsurance from a bankI in t = 0 the entrepreneur contracts with a bank a credit lineequal to 20. If in t = 1 the overrun occurs, the credit line isdrawn. The bank cannot renege. It pays 20 and becomes thesenior creditor: the old investors get nothing and the bankgets 12 in t = 2

I in t = 0, to commit to the credit line, the bank asks a feeequal to 4

I the bank is �ne. It makes zero expected pro�ts: it loses if thecredit line is drawn, it gains if no overrun occurs

4 (1/2)20+ (1/2)12 = 0

I in t = 0 investors must now contribute more than 2 (thedi¤erence between the cost of the project and theentrepreneur�s contribution). Now they must also pay thebank�s fee. Thus they must contribute 2+ 4 = 6

I investors are happy to contribute 6 because 6 = (1/2)1266

�

Insuring through a credit line

I Alternatively, assume that the bank, rather than being paid afee, is paid in shares of the �rm. The �rm issues 4 moreshares (beyond the 2 bought by investors) so that the totalcapital of the project is now 6 :I 4 = (2/3)6 is the capital contributed by the bankI 2 = (1/3)6 is the capital contributed by investors

I Expected returns (computed as of t = 0) equal the amount ofcapital invested. The expected return for investors is 2, equalto the amount they paid to buy shares. The expected returnof the bank is zero, since the shares were given to the bank forfree (in exchange for its commitment to �nance an overrun):I investors:(1/2)(1/3)12+ (1/2)(1/3)0 = 2I bank: (1/2) [(2/3)12] + (1/2) [ 20+ 12] = 0

67

�

The problem of time inconsistency

I Remember that in t = 1 the bank cannot renege on the creditline

I Come t = 1 �nancing the overrun is a money-losing operation:the bank would not be willing to do it unless it is bound by acontract� an example of a situation of time inconsistency

I Thus the credit line must be pre-arranged in t = 0

68

Macroeconomics

I Where does the bank �nd the 20 it is committed to contributeto the project in the event of an overrun?

I Assume that there are many �rms and that their liquidityshocks are uncorrelated: half face an overrun, half do not. Inother words there is no macroeconomic (or aggregate) shock

I Is there enough private liquidity in this economy to avoidine¢ cient liquidations, or do you need the "government" tostep in to avoid liquidations?

69

Diversi�cationI Assume the number of �rms is normalized to 1I In t = 0 the bank receives 2/3 of the shares of all �rms� inexchange for the commitment to provide liquidity in t = 1 tothose �rms (1/2 of all �rms) who will need it

I In t = 1 the bank, to honor its commitment, needs(1/2) 20 = 10

I The value of the bank�s portfolio (the value of the shares itowns) is: [(1/2) 12] + [(1/2) (2/3)12] = 10I [(1/2) 12] is the value of the bank�s shares in the �rms thathave a liquidity shock, where old shareholders will receivenothing and the bank will receive the entire pledgeable output;

I [(1/2) (4/6)12] is the value of the bank�s shares in the �rmsthat do not have a liquidity shock, and where the bank willshare pledgeable output with small shareholders

I By selling its entire portfolio (assuming the existence of amarket where the bank can do this) the bank obtains enoughliquidity to "recapitalize" half the �rms.70

Diversi�cation

If liquidity shocks are uncorrelated there is always enough insideliquidity and no project will ever be abandoned. What could gowrong?

71

The need for banking supervisionInside liquidity need not only be su¢ cient in the aggregate. Italso needs to be dispatched to those who need itI this condition breaks down if banks are not perfectly diversi�edI in the previous example there is only one bank: shocks cancelout in the aggregate, thus the bank is perfectly diversi�ed

I but consider a situation where there are two �rms and twobanks each extending a credit line to one �rm onlyI there is no aggregate liquidity shock: one �rm faces an overrunand draws on its credit line; the other pays the commitmentfee but does not draw because it has no overrun

I one bank makes a pro�t of 4 (the commitment fee), the othera loss of 4

I the �rm which faces an overrun cannot rely on its bank to�nance it and must fold up its project

I there is still enough liquidity in the aggregate, but it is notdispatched to the �rm that needs it because the bank whichmakes a pro�t has no incentive to give it up, transfer it to theother so that this can deliver on its committed credit line72

Liquidity crises: summing up

The lesson from this example is that inside liquidity may beinsu¢ cient to prevent liquidation of otherwise productive projects,even absent macroeconomic shocks. The government has two waysto deal with this

I it can use regulation to make sure that all banks are perfectlydiversi�ed, so that none is exposed to idiosyncratic shocks.This is the superior, though probably unrealistic solution

I alternatively, if regulation fails to achieve perfectdiversi�cation, it can step in to provide outside liquidity tothose �rms to which liquidity fails to be dispatched

Why can the government provide "outside liquidity" when theprivate sector cannot? Because the government can raise funds int = 1 by taxing citizens and promising to pay them back in t = 2

73

Borrowing with collateral, leverage and the ampli�cationand persistence of real shocks

I Why and through which channels can the �nancial marketamplify a shock that hits the real economy, for instance ashock to productivity?

I Why does leverage arise and how does it amplify shocks

I Why shocks do not die out immediately� i.e. they arepersistent

[Nobu Kioyotaki and John Moore, "Credit Cycles", Journal ofPolitcal Economy, 1997]

74

A model of Entrepreneurs and LandlordsI The economy has a �xed quantity of land, k that can be used togrow fruit

I Some land is farmed by Entrepreneurs, (E ), the rest of the land isfarmed by Landlords, (L): kL + kE = k

Entrepreneurs: their technology to grow fruit is yE akEI t = t 1with a (which is a measure of their productivity) constant andrelatively high. Thus E have a very e¢ cient technology withconstant returns. But they own no land: to produce they needto buy the land from landlords

I Landlords: have a more traditional decreasing-returnstechnology: yL L

t = f (kt 1), f0 0

0, f

0 0. Decreasing returns

means that their productivity is lower the larger the portion ofland they farm. Thus beyond some point they are willing tosell their land to E . How much land they farm thus dependson how much they sell to E . The larger is kEt (the land farmedby E ) the smaller is the land farmed by L, and thus the higherits productivity

I it takes one period to grow fruit: kL, E produces fruit in tt 175

�

�

�

EntrepreneursI E 0s resources (their net worth) are not su¢ cient to buy the landthey wish to farm

I To buy the land E borrow from L. So L sells land to E and at thesame time �nances E 0s purchase

I De�ne q the price of land and b the amount E borrows from LI Loans are for one period. The gross interest rate is R : if youborrow b the following period you need to repay Rb (the interestplus the principal). R is exogenous

I E0s budget constraint

akEt 1 Rbt 1 + q E Etkt 1 + bt � qtkt

which can be re-written as

qt�kEt kEt akE + (b Rb )1

�� t 1 t t 1

the term on the left is E0s net purchase of land; the terms on the

right are, respectively, E0s income and its net borrowing76

� � � �

� � � � �

Entrepreneurs�collateral constraint

I L lend to E only if the loans are guaranteed by su¢ cient collateral

I The collateral is land: if E fails to repay the loan, L keeps the land

Rbt � qt+1kEt

I Rbt is how much E needs to repay in (t + 1)EI qt+1kt is the value, at time (t + 1) , when the loan is repaid,

of the land used as collateral

77

78

How much will E borrow and how much land will E buy ?I E will�borrow as� much as they can given the constraintbt = qt+1kEt /R

I Replacing bt into E0s budget constraint we determine how much

land E will buyE E E(qt � qt+1/R) kt = (qt + a) kt�1 � Rbt�1 = akt�1

E spend their entire net worth, (q + a) kE Et t�1 � Rbt�1 = akt�1,

on the di¤erence between the cost of new land, qtkEt , and theamount they can borrow against each unit of land they buy,(qt+1/R)

I (qt � qt+1/R) is the downpayment E pays when buying the land:you pay qt to buy a unit of land but you can borrow qt+1/R , thuswhat you need to pay upfront is (qt � qt+1/R) per unit of landyou buy. In other words

I E buys land up to the point at which the required downpayment iscovered by E

0s net worth. The amount of land E buys is thus

kEt = akE 1t�1 (qt � qt+1/R)

�

Borrowing and leverage

kEakEt

t =1 net worth

=(qt qt+1/R)

= leverage(1 / leverage)

� net worth

I Borrowing, Entrepreneurs "leverage" their net worth buying kEt net worth

I The smaller the downpayment, (qt qt+1/R) , they are requiredto put up, the larger the amount of land they can buy for any valueof their net worth

79

��

�

LandlordsI L farms land up to the point at which the productivity of the landthey farm equals the opportunity cost� what they would earn ifinstead of farming they sold the land to E in t (and buy it t + 1)

1Rf 0�kLt�= qt qt+1/R = ut (kLt ) = ut (k kEt )

on the left is L0s return per unit of land they farm (discounted by Rbecause it takes one period for land to produce fruit). On the rightis the alternative: instead of farming the land, L can sell it in t andbuy it back in t + 1 at price qt+1 (discounted because you buy itback one period later). This alternative is the opportunity cost (alsocalled user cost, ut )

I ut plays a dual role. It is L0s opportunity cost of farming a unit of

land, but it is also the required downpayment per unit of land Ebuys

I This condition determines how much land L farm1Rf 0(k kEt ) = ut (k kEt )

80

� �

� �

81

Steady State

I The economy is in steady state when qt = qt�1 = q� andkEt = k

Et�1 = k

E �

I From qt � q Lt+1/R = ut (kt ) and (qt � qt+1/R) kEt = akEt�1

we can thus determine the steady state values q� and u�

R � 1q� = u� = a

R

I From the condition determining how much land L farms,1 (R f0 k � kEt ) = ut we �nd kE �

I Finally, using the collateral constraint, bt =�qt+1kEt /R

ab� =

�kE �

R � 1

Steady state

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82

Leverage and Ampli�cation of shocks

kEakEt

t =1 leve E= leverage net worth = rage ak

(q q t 1t t+1/R)

� �

I Assume E su¤er a shock to their net worth: for instance theirproductivity, a, fallsI because leverage 1, kEt falls by moreI leverage ampli�es shocks

I But leverage itself will change when a fallsI assume when the shock occurs we are around the steady stateI remember that in steady state q� R= a. q faR 1

� lls when afalls

I the fall in q� produces a capital loss on the land owned by Ethat reduces leverage and further ampli�es the shock to a

83

�� �

�

Persistence

I As a result of the fall in a, E enter the following period with lowernet worth

I Thus the shock does not die out immediately: it propagates to thefollowing period

84

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14.02 Principles of MacroeconomicsSpring 2014

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